THREE KINDS OF UTILITY FUNCTIONS FROM THE MEASURE CONCEPT

In this paper we analyze the existence of three different kinds of continuous numerical representations for binary relations by using a finite measure defined on the space of alternatives. Each one of these kinds of representation is suitable for a different class of binary relations. Thus we obtain the traditional utility function for continuous preorders and weaker representations by dropping continuity or transitivity conditions (in particular, for lexicographical orders or acyclic relations).